How to make a distinction between item feature and environment feature?
I am curious to know if I can put the economy feature such as 'national interest rate' or 'unemployment rate' besides each stocks' features.


The variables are macro-econometric and they, in general, seem to have some influence on stocks' prices. This inclusion might as well increase your model's prediction accuracy. You can definitely use them as predictors. As mentioned in comments - Experimentation is the way to go.


  Can I feed the data to my neural network like the table above?


In general, you can have any kind of numeric variables as input to a neural network. Things will work out fine. The important thing is the selection of relevant predictor variables that, potentially, have some relationship with the response variable.